The following description includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication specifically or implicitly referenced is prior art.
Harmonic analysis involves the representation of functions or signals as superpositions of basic waves. Harmonic analysis has found application in a great many fields, including signal processing, quantum mechanics, and neuroscience.
Fourier analysis is a subset of harmonic analysis, in which signals are decomposed into real and imaginary components using a transform. The terms “transforms” and “transformation” are used herein to mean decomposition of a signal into a multiple components in the same or a different domain. For example, a Hilbert transform converts a function in one domain into a function in the same domain. In contrast, a Fourier Series or a Discrete-time Fourier transform (DTFT) transform a time series into a frequency spectrum. Transforms can be applied to time domains, spatial frequencies, and indeed to nearly any function domain. Various transforms are currently used for compression, filtering, frequency balancing, encryption, and for other purposes. Although transforms are usually mathematically based, transforms can also implemented in electronics, as for example, using a parallel pair of serially cascaded biquad filters.
Components produced by transformation can be processed separately, and synthesized (inverse-transformed) back together again. Transformed signals are not, however, always synthesized back to equivalent originals. MP3 compressed audio files, for example, contain only the real component of the original signal, not the imaginary component, and thus sustain significant loss in sound quality when being rendered to a listener. Additional losses can arise from the compression technology, resulting in sizzling, distortion, and flat, two dimensional sounds. Thus, there is a need to present such transformed audio files to a listener in a manner that is at least perceived to have a quality closer to that of the source of the original recording than a standard rendering.
In the case of video files, typical PEG compression applies a variant of a Fourier transformation (discrete cosine transform) to small square pieces of a digital image. The Fourier components of each square are rounded to lower arithmetic precision, and weak components are eliminated entirely, so that the remaining components can be stored very compactly. In normal image reconstruction, each image square is reassembled from the preserved approximate Fourier-transformed components, which are then synthesized to produce an approximation of the original image. Although rendering of a PEG-compressed file includes both components, current display technologies can cause blur and other distortions, due to inadequate pixel response time on LCD displays, resolution sampling methods, telecine processing by studios, and compression artifacts. These problems are especially pronounced with High Definition 4K and other large files. With the advent of LCD displays, motion blur has become even more of a problem due to sample-and-hold nature of the displays.
Several attempts have been made to resolve these distortions with respect to video files. ClearLCD™ and Clear Motion Rate™ technologies from Philips™ and Samsung™, for example, use a strobed backlight to reduce blurring. However, the existing solutions are limited to specific applications rather than being globally applicable. Thus, there is also a need to render compressed video files to a viewer in a manner that is at least perceived to have a quality closer to that of the source of the recording than a standard rendering.
With respect to biometrics, it is known to use brain waves to control physical or virtual objects, or to achieve a particular mental state, as for example a delta sleep state. Typically, this is accomplished by using the waves to trigger a beep, color on a display, movement of a mechanical arm, or other highly simplified indicia of a desired result. In so doing, a great deal of useful information about the subject's current psychology and cognition is eliminated. There is consequently a need to provide much more sophisticated feedback to a brain wave subject than is currently known.
Regardless of what type of signals are being processed (auditory, video, brain waves, etc) there is still a problem with the speed in which transforms and synthetic operations can be applied to complex signals, especially on a consumer device such as a laptop, tablet or cellphone. Presenting results to a listener, viewer, subject or other user even five, two, or one second after the signal is generated (or rendered from a data file) may be too slow to provide sufficient feedback to adequately manipulate the rendering in what appears to be a real-time fashion. Thus, there is a need for faster processing hardware and software to achieve the appearance of real-time operation and feedback.